Materials with self-adaptive mechanical responses have long been sought after in material science. Using computer simulations, researchers at the Tata Institute of Fundamental Research (TIFR), Hyderabad, now show how such adaptive behavior can emerge in active glasses, which are widely used as models for biological tissues. The findings provide new insights—ranging from how cells might regulate their glassiness to aiding in the design of new metamaterials.
Glasses (or amorphous solids) are materials whose components lack any particular ordering. Contrast this with a crystal, where atoms are arranged in neat, repeating patterns on a well-defined lattice. While crystals are ordered and nearly perfect, amorphous materials are defined by their disorder. When these disordered materials are composed of components that can utilize internal energy reserves and move autonomously, they form what are known as active glasses. Such systems are abundant in environments where particles are tightly packed and possess chemical reserves—for instance, epithelial cells or bacterial colonies.
However, not all glasses are created equal. Depending on their preparation, the same material can form glasses with widely varying mechanical properties. This history dependence is a hallmark of non-equilibrium systems—they remember how they were prepared! To prepare a glass, start with a liquid (almost any liquid will do) and cool it rapidly past its melting point. If the cooling is fast enough, crystallization can be avoided, resulting in a supercooled liquid. As the temperature continues to drop, there is an empirically defined temperature below which the dynamics slow down so dramatically that tracking the system in any detail becomes infeasible. This is the famous glass transition temperature. Below this point, the system is effectively in an arrested state. And voilà, what you have now is a glass.
What is particularly interesting is that, although the dynamics have changed drastically, structurally the system hasn't changed much. A clear understanding of how this crossover to an arrested state occurs is still lacking. Incidentally, the nature of this transition was once referred to by the Nobel Laureate P. W. Anderson as "the deepest and most interesting unsolved problem in solid-state theory" [Science, 1995]—and it still remains elusive.
Depending on how quickly or slowly you cool across this glass transition temperature, you obtain glasses with different mechanical properties. Generally, slower cooling results in well-annealed glasses, which are brittle (systems that break abruptly with a sharp snap under external loading), whereas faster cooling results in poorly annealed glasses, which are more ductile (systems that elongate and form necks before eventually breaking). Another way to visualize this is through an energy landscape, with barriers (hills) separating local minima (valleys). Any glass configuration can be thought of as being stuck in one of these many local minima, with barriers preventing it from transitioning and exploring other lower energy states. Better cooling while creating the glass leads the system to a deeper minimum in this landscape.
Sharma and Karmakar discovered that imparting additional motility to some components of a poorly annealed glass induces further annealing in the system, taking it to progressively lower regions of the landscape. This is reflected as a gradual decrease in the system's potential energy. They demonstrated that the local rearrangements caused by activity in a glass can anneal the system enough to transform an initially ductile material into a brittle one. In essence, the researchers found that active dynamics can provide a means to traverse the energy landscape more effectively.
A corollary of this is that the enhanced aging observed in active glasses could partially account for some of the mechanical changes seen in aging and maturing tissues. Thus, drawing inspiration from biological tissues, one might design new metamaterials that incorporate active constituents to regulate their brittleness throughout their lifecycle.
Even more interestingly, the study found that active glasses share many of the same phenomena observed in glasses subjected to oscillatory (or cyclic) shear. To briefly illustrate cyclic shear deformation, imagine taking a solid box and fixing its base so that it cannot move. Now, hold the top and repeatedly push and pull on it along a fixed direction parallel to the top face. This is a simplified caricature of an oscillatory shear deformation. The study found that the amplitude and frequency of such an oscillation imposed on passive amorphous solids could be effectively mapped to the strength of active forces and their persistence time, respectively, in active glasses.
Besides showing mechanical annealing, another characteristic of glasses under oscillatory shear is that, after repeated cycles, the deformation amplitude becomes imprinted onto the system. This imprint can later be "read" out using sophisticated techniques. Remarkably, similar memory effects were also discovered in the case of active glasses, using slightly different but analogous reading protocols. Since activity in assemblies of cells is generally controlled by their metabolism, the memory effects observed could provide insights into how learning and metabolic needs are connected. Other similarities include the system's transition from a stuck state to a fluidized state at large driving values. This fluidization in active glasses has been extensively studied in the literature and is crucial for understanding the biophysics of wound healing and morphogenesis, both of which involve mass cell migration.
The fact that systems as complex as active glasses can essentially be mapped onto ordinary glasses under oscillatory shear implies that researchers can now utilize the extensive toolbox developed for understanding amorphous solids to study biophysical systems.
This study reveals a deep analogy between active glasses and cyclically driven amorphous solids, establishing internal activity as a novel means to anneal glasses. However, this method struggles to match the performance of dedicated in-silico annealing techniques like Swap Monte Carlo. Non-local moves, such as swapping particles over arbitrary distances, allow Swap Monte Carlo to reach extremely low-energy states that remain out of reach for local methods like activity-induced annealing. Further exploration is needed to determine whether such local methods can become more competitive with other dedicated techniques or be used in tandem to further equilibrate glasses. This, along with exploring memory and learning effects in active systems, presents promising avenues for future research.
